{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:MDHKEVYITWRR4XYY5IXHWKSCDA","short_pith_number":"pith:MDHKEVYI","schema_version":"1.0","canonical_sha256":"60cea257089da31e5f18ea2e7b2a4218329811a05ec148577ff2e959e141e9e0","source":{"kind":"arxiv","id":"1009.0530","version":2},"attestation_state":"computed","paper":{"title":"High-dimensional covariance estimation based on Gaussian graphical models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Min Xu, Peter Buhlmann, Philipp Rutimann, Shuheng Zhou","submitted_at":"2010-09-02T20:06:40Z","abstract_excerpt":"Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\\ell_1$-penalization methods. We propose and study the following method. We combine a multiple regression approach with ideas of thresholding and refitting: first we infer a sparse undirected graphical model structure via thresholding of each among many $\\ell_1$-norm penalized regression functions; we then estimate the covariance matrix and its inverse using the maximum likelihood estimator. We show that under suitable conditions, this approach yields consis"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1009.0530","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2010-09-02T20:06:40Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"2f4e8214580fb7d66f38194d79835e1ca5ebb12357223cb38269f6e7e9adcda4","abstract_canon_sha256":"6ad0a94ac9283a5eb68ecc3482e5489dbb83d8ffdde278bbe71170656f70213f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:55.004086Z","signature_b64":"9OEtOJLmGN7kOIwKEycZwYWl8lGXxpqjnXXviSZS4GhVZKfV+mTl1QqyihRAcUU8ZCEWiKgwwADMTgNak4TIAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60cea257089da31e5f18ea2e7b2a4218329811a05ec148577ff2e959e141e9e0","last_reissued_at":"2026-05-18T04:04:55.003626Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:55.003626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"High-dimensional covariance estimation based on Gaussian graphical models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"stat.ML","authors_text":"Min Xu, Peter Buhlmann, Philipp Rutimann, Shuheng Zhou","submitted_at":"2010-09-02T20:06:40Z","abstract_excerpt":"Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\\ell_1$-penalization methods. We propose and study the following method. We combine a multiple regression approach with ideas of thresholding and refitting: first we infer a sparse undirected graphical model structure via thresholding of each among many $\\ell_1$-norm penalized regression functions; we then estimate the covariance matrix and its inverse using the maximum likelihood estimator. We show that under suitable conditions, this approach yields consis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0530","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1009.0530","created_at":"2026-05-18T04:04:55.003687+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.0530v2","created_at":"2026-05-18T04:04:55.003687+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0530","created_at":"2026-05-18T04:04:55.003687+00:00"},{"alias_kind":"pith_short_12","alias_value":"MDHKEVYITWRR","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_16","alias_value":"MDHKEVYITWRR4XYY","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_8","alias_value":"MDHKEVYI","created_at":"2026-05-18T12:26:10.704358+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MDHKEVYITWRR4XYY5IXHWKSCDA","json":"https://pith.science/pith/MDHKEVYITWRR4XYY5IXHWKSCDA.json","graph_json":"https://pith.science/api/pith-number/MDHKEVYITWRR4XYY5IXHWKSCDA/graph.json","events_json":"https://pith.science/api/pith-number/MDHKEVYITWRR4XYY5IXHWKSCDA/events.json","paper":"https://pith.science/paper/MDHKEVYI"},"agent_actions":{"view_html":"https://pith.science/pith/MDHKEVYITWRR4XYY5IXHWKSCDA","download_json":"https://pith.science/pith/MDHKEVYITWRR4XYY5IXHWKSCDA.json","view_paper":"https://pith.science/paper/MDHKEVYI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.0530&json=true","fetch_graph":"https://pith.science/api/pith-number/MDHKEVYITWRR4XYY5IXHWKSCDA/graph.json","fetch_events":"https://pith.science/api/pith-number/MDHKEVYITWRR4XYY5IXHWKSCDA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MDHKEVYITWRR4XYY5IXHWKSCDA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MDHKEVYITWRR4XYY5IXHWKSCDA/action/storage_attestation","attest_author":"https://pith.science/pith/MDHKEVYITWRR4XYY5IXHWKSCDA/action/author_attestation","sign_citation":"https://pith.science/pith/MDHKEVYITWRR4XYY5IXHWKSCDA/action/citation_signature","submit_replication":"https://pith.science/pith/MDHKEVYITWRR4XYY5IXHWKSCDA/action/replication_record"}},"created_at":"2026-05-18T04:04:55.003687+00:00","updated_at":"2026-05-18T04:04:55.003687+00:00"}